The sap that comes from sugar maple trees is mostly water, with about $2\%$ sucrose $)$ by mass. The sap is then concentrated to about $66\%$ sucrose, resulting in the thick maple syrup you pour on pancakes. Traditionally, the raw sap was boiled to concentrate it$,$ but many producers today first use reverse osmosis to create a more concentrated solution that requires less boiling. A kit for a small producer uses a pressure of $510$kPa across a membrane. Assume the total density of the concentrate is very close to that of water.

Part A

If $25C$ sap containing $2\mathrm{.}0\%$ sucrose enters the system, what is the maximum sucrose concentration of the resulting concentrate?

Express your answer as a percentage.

$f_{\text{m}\text{a}\text{x}}=$

$$

$\%$

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